c - J T ¡ y / ^ / i r

T H E

RHEOLOGY LEAFLET

T i a v z a § e i

P u b l i c a t i o n of the

SOCIETY OF RHEOLOGY No. 7 November, 1938

T H E R H E O L O G Y L E A F L E T

P u b l i s h e d Qua r t e r l y B y

T h e Soc ie ty of Rheo logy 175 F i f th A v e n u e

N e w Y o r k City

E d i t o r :

W h e e l e r P. D a v e y P e n n s y l v a n i a S ta t e College S ta te College P e n n s y l v a n i a

N o n - M e m b e r Subsc r ip t ions S2 .00 Annua l ly

Single C o p i e s : 75c apiece

Address All C o m m u n i c a t i o n s to the Edi tor

THE RHEOLOGY LEAFLET No. 7 rnvra §ei November , 1936

TENTH ANNUAL MEETING

This issue of the Leaflet is in tended to serve pr imari ly as a pro-g r a m f o r the annua l mee t ing of the Society, which is to be held at the Mellon Ins t i tu te of Industr ia l Research, Univers i ty of P i t t sburgh , on December 28 to 29. O u r technical sessions will be held at the Mellon Ins t i tu te Audi to r ium, 4 4 0 0 F i f th Avenue , P i t t sburgh , which has been m a d e available t o us t h rough the cour tesy of the Univers i ty of Pit ts-burgh .

T h e t h a n k s of the Society are also due t o the C o m m i t t e e on Ar rangements , cons t i tu ted as fo l lows :

Dr . E. W a r d Til lotson, C h a i r m a n , Dr. A. Nadai , Dr. E. Hutchisson , Dr . G. R. S t u r m .

T h e p r o g r a m appears on the pages fo l lowing. Th i s is the f ru i t of the labors of the P r o g r a m Commi t t e e , consis t ing o f :

Mr. H. R. Lillie, Cha i rman , Prof . E. C. B ingham, Dr. J . H. Dillon, Dr. E. Hutchisson, Dr . E. W . Til lotson, Mr. R. N. Trax le r and Dr . H. F . Wakef ie ld .

Along with our o w n p r o g r a m is given tha t f o r a session of the Chemical Engineer ing Sympos ium, which will be held in the Little Thea t re of the Carneg ie Ins t i tu te of T e c h n o l o g y on the a f t e r n o o n of December 28. Th i s session is par t of a mee t ing of the Divis ion of In-dustr ial and Engineer ing Chemis t ry of the Amer ican Chemical Society. T h e Society of Rheology has collaborated wi th the C o m m i t t e e of the Chemical Engineer ing S y m p o s i u m in p repar ing the p rog ram f o r this session, and t w o of the f o u r pape r s scheduled are by our members . T h e a f t e rnoon of December 28 is t he re fo re be ing left f r ee t o permi t a t tend-ance at the S y m p o s i u m .

In addit ion t o the p rogram, this issue of the Leafle t conta ins ab-s t racts of the papers to be presented at the meet ing , and also the revised repor t of the C o m m i t t e e on Def in i t ions and Nomenc la tu re . T h e orig-inal repor t w a s published in Leafle t No. 1, May 1937, and discussed at the last annua l mee t ing . As a result of this discussion, the Society adopted a resolut ion re fe r r ing t h e repor t to the C o m m i t t e e f o r revision. T h e repor t as g iven here has been revised in the light of the discussion on which this act ion was based, and is n o w of fe red to the Society for adopt ion . Discussion of the repor t is scheduled as par t of the p rog ram f o r the session to be held the m o r n i n g of December 29.

1.

P R O G R A M

TENTH ANNUAL MEETING

MELLON INSTITUTE, PITTSBURGH, PA.

December 28-29, 1938

December 28.

9 : 0 0 - 9 : 4 5 A. M. Registrat ion at Beliefield A v e n u e Ent rance , Mellon Ins t i tu te of Industr ial Research.

1 0 : 0 0 A . M . Technical Session — Mellon Inst i tute . Gree t ing by E. W . Til lotson, Assistant Director , Mellon Inst i tute .

1 0 : 1 5 M. L. Huggins , E a s t m a n Kodak Co., " T h e S taudinger Viscosity L a w . "

1 0 : 4 0 E. C. B i n g h a m and Harold C. Adams, La faye t t e College, "Flu id i ty of Electrolytic So lu t ions . "

1 1 : 0 5 P. W . Kinney, A r m s t r o n g Cork Co., " T h e Re-lation of Fluidi ty to Vo lume in O r g a n i c Liquids ."

1 1 : 3 0 P. S. Roller, U. S. Bureau of Mines, "Plas t ic F low of Dispersions, and a New Approach to the S tudy of Plas t ic i ty ."

1 2 : 0 0 M. A. G e m a n t , Univers i ty of Wisconsin , "Mobil-ity of Ions in Plastic Dielectr ics ."

1 2 : 3 0 P . M. Luncheon

2 : 0 0 P . M. Chemica l Engineer ing S y m p o s i u m of the Am-erican Chemica l Society. T o be held at the "Lit t le T h e a t e r " , Carnegie Inst i tute of Tech-nology, located about one-half mile f r o m Mel-lon Inst i tute. T h e fo l lowing papers will be p r e sen t ed :

M. D. Hersey (Soc. Rheol . ) , Kingsbury Ma-chine W o r k s , "Dimens iona l Analysis Applied to Fluid Mot ion ."

M. P. O 'Br i en , R. G. Folsom and F. Jonas sen (A .C .S . ) , Univ . of Cal., "F lu id Resistance in P ipes . "

2.

R. H. Ewell (Soc. Rheo l . ) , P u r d u e Univ. , " T h e Viscosity of Liquid Mix tu res : Ideal and non-Ideal Behav io r . "

R. H. Wi lhe lm, D. M. W r o u g h t o n , and W . E. Loeffel (A.C.S . ) , Pr ince ton Univ. , " F l o w of Suspens ions : I. A Concen t r i c Motor Dr iven Vis-come te r ; II. F low of Suspens ions t h r o u g h P ipes . "

6 : 3 0 P. M. Rheology Dinner — Webs te r Hall Hotel .

December 29.

8 : 4 5 A . M . Technical Session, Mellon Inst i tute .

8 : 4 5 E. P. Irany, Shawin igan Chemicals , Ltd., Can-ada, "Viscosi ty and C o n s t i t u t i o n . "

9 : 3 0 A. Kirkpatr ick, Monsan to Chemical Co., " S o m e Rela t ions be tween Chemical S t r u c t u r e and Plast icizing Effec t .

9 : 5 0 F. E. Dar t and E. G u t h , Univers i ty of Notre D a m e , " T h e Thermoelas t ic Proper t ies and the Equat ion of S ta te of R u b b e r . "

1 0 : 1 0 R. H. Ewell, P u r d u e Univ. , "Theore t ica l Con-siderat ion Conce rn ing the Viscosity of Binary Silicate Glasses . "

1 0 : 3 0 R- B. D o w , Pennsy lvan ia S ta te College, "Re-cent D e v e l o p m e n t s in the S tudy of Viscosity of Lubr ica t ing Oi ls at High P res su re . "

1 0 : 5 0 H. Eyring, J . F. Kinkaid and D. Frisch, Pr ince-ton Univ. , "P re s su re and T e m p e r a t u r e Ef fec t s on Viscosi ty."

1 1 : 1 5 R- B. D o w , Pennsy lvan ia State College, "Vis-cosity of C C I 4 - C S 2 Mixtures of Liquids at High P re s su re . "

1 1 : 4 5 Report of C o m m i t t e e on Def in i t ions and Nom-encla ture .

1 2 : 3 0 P . M. L u n c h e o n — Business Meet ing.

2 : 0 0 P . M. P lan t Tr ips to be announced at the meet ing .

3.

ABSTRACTS O F PAPERS

The Staudinger Viscosity Law Maurice L. Huggins, Eas tman Kodak Co.

An equat ion has recently ( J . Phys . Chem. , 42 , 9 1 1 ( 1 9 3 8 ) ) been derived for the specific viscosity of a dilute solution of " r andom-ly-kinked" chain molecules, which, fo r long chains and small concen-trations, is of the same form as Staudinger ' s empirical " l a w " : H 8 p * k s n c

The validity of this equat ion fo r actual solutions, and the na ture and magni tude of the derivat ions to be expected will be discussed, also methods fo r the theoretical and exper imenta l determinat ion of the constant , 1 % .

Effec t s due to the na ture of the solvent, of the repeat ing uni ts in the chain^ and of the end groups will be considered and illustrated with exper imenta l data.

The Relation of Fluidity to Volume in Organic Liquids P. W . Kinney, Armst rong Cork C o m p a n y

Viscosity data have been studied for a large number of compounds , including several members of the homologous series of normal ali-phatic hydrocarbons, ethers, thiols, mercaptans , bromides, acids, alco-hols and esters. The results are utilized in a critical examinat ion of the validity of t w o expressions relating viscosity to molecular volume. O n e is the hyperbolic equa t ion :

V = A i -B/*> + C

in which V and are molecular vo lume and fluidity. The other is the Batschinski express ion:

= C / ( v - < o )

where ij and (v-o> ) are viscosity and " f r ee vo lume . " The two ex-pressions differ only in the correction t e rm ( -B/(>). Results s h o w : (1 ) the hyperbolic expression holds fo r all c o m p o u n d s studied, while the Batschinski equat ion fails in the case of those either assoc-iated or of high molecular weigh t ; (2) A varies parabolically, and B exponential ly, with the n u m b e r of carbon a toms; (3 ) C is additive and closely related to Batschinski 's limiting volume w ; (4) the "corrected f ree vo lume" varies exponential ly with the number of carbon a toms in an homologous series; and (5 ) the constants A, B, and C can be utilized in calculating association in associated series, or in predicting viscosities in undetermined members of the various homologous series.

4.

Plastic Flow of Dispersions, and a New Approach to the Study of Plasticity.

Paul S. Roller, U. S. Bureau of Mines.

It is a rgued tha t s ince plast ici ty is the p rope r ty de f in ing ease of de fo rma t ion , the variables in which it is expressed should be stress and p e r m a n e n t s t rain, ra ther than shear ing stress and ra te of shear . This con ten t ion is based on expe r imen t s measu r ing p e r m a n e n t defor -mat ion under compress ive stress, us ing plastic dispers ions con ta in ing part icles r ang ing f r o m microscopic to g r anu la r in size. A general law was f o u n d to hold :

a p / p m i o g ( p / p 0 ) " d v / y " l o g ( h / h 0 )

where d p and d v are inc rements of pressure p and vo lume v and h is sample height . K is called the coeff ic ient of ren i tence as a m e a s u r e of resistance to con t inued plastic f low, whi le p is identif ied with yield value . T h e cons tan t s K and p un ique ly de te rmine the plastic behav-ior. The f o r m e r is dependen t upon the sort of phase present but inde-penden t of the relative a m o u n t , while p d e p e n d s on the liquid-solid ratio. Highly plastic mater ia ls are character ized by a K less than abou t uni ty , K being as high as 35 for s o m e only slightly plastic dis-pers ions. If K is too large, desired workabi l i ty canno t be secured by any pract icable increase in solid-liquid ratio. Cohes ion is f o u n d to be measu red by the a m o u n t of l iquid re ta ined at a specified yield value in dispers ions of a b o u t the s ame va lue of K. Th i s liquid re tent ion (at cons tan t p ) appears to be related to f ineness of solid subdivis ion. Rate of stress a f f ec t s the plastic f l ow cons tan t s bu t little. A theoretical t r e a t m e n t of plastic f l ow in dispersions, f r o m the s tandpoin t of fac to rs de te rmin ing a t t ract ive forces be tween part icles (e lectrokinet ic potent -ial, solvat ion and dispers i ty) leads to the deduct ion tha t the grea te r the force of a t t ract ion at uni t dis tance of separa t ion of particles, the great -er the plasticity. Expe r imen t s con f i rm the theoret ical ly expected results.

Mobility of Ions in Plastic Dielectrics A. G e m a n t , Univers i ty of Wisconsin

T h e paper is concerned with ionic mobil i ty in v i t reous dielectrics, which genera l ly exhibit a f ini te plasticity. T h e f u n d a m e n t a l idea is to deal with the de fo rmat ion as caused by the mot ion of an ion in the same way as macroscopic d e f o r m a t i o n s of the plastic are dealt with. Th i s lat ter can be described by m e a n s of th ree cons t an t s of the mater ial , n a m e l y plasticity, elasticity and solid fr ict ion, and the s ame should hold for the molecular de fo rma t ion a round a m o v i n g ion.

5.

In app ly ing this idea to the ionic mot ion in a d. c. field, it appears that , a l though the largest par t of the work done by the field is conver t -ed into heat , a small f rac t ion is retained by the ion in the f o r m of kinetic energy . Th i s f rac t ion increases with increasing field s t rength . If the a m o u n t of ene rgy collected in this way reaches the ionizat ion energy, ionizat ion will set in, leading to an increase of the electrical conduct iv-ity. Th i s p h e n o m e n o n has been observed wi th a great n u m b e r of diel-ectric mater ia ls . T h e theory requi res the ef fec t to become appreciable be tween 1 0 4 and lCf5 Vo l t s / cm, in ag reemen t with observat ions .

In ex t end ing the t heo ry to ionic mobil i ty in an a. c. field, it appea r s that plasticity loses its s ignif icance and the losses are control led only by the solid fr ic t ion. T h e dielectric loss fac tor , or the equiva len t a. c. conduc t iv i ty can be c o m p u t e d by m e a n s of the solid fr ict ion coeff ic-ients, as k n o w n f r o m mechanical vibrat ions, and the a., c. conduct iv-ity t u r n s ou t to be t w o or th ree orders larger than the d. c. conduc t iv i ty . Th i s is a fact well k n o w n f r o m exper imenta l da ta . T h u s the theory ac-coun t s for the dielectric losses even in the absence of any special mechan i sm, dipolar rotat ion, fo r ins tance.

Dimensional Analysis Applied to Fluid Motion Mayo D. Hersey, Kingsbury Machine W o r k s

Th is pape r o f f e r s a brief review of a well-established me thod not yet as widely used as it deserves to be. T h e d imens ional m e t h o d is he lp fu l as a s tep in the deve lopmen t and checking of theoret ical equa-tions, but f inds its greatest value in the p l ann ing and in terpre ta t ion of exper imenta l work .

T h e con t r ibu t ions of Fourier , the late Lord Rayleigh, Edgar Buck ingham, and o thers are out l ined. T h e practical use of the theorem of "d imens ion less var iab les" in reduc ing the n u m b e r of fac to rs re-qui r ing exper imenta l var ia t ion is expla ined, closely fo l lowing Buck-i n g h a m ' s t r ea tmen t . Its ana logy with the phase-rule in certain par t icu-lars is indicated, also its use in ex t rapo la t ing and genera l iz ing empirical equa t ions . Model expe r imen t s and dynamica l s imilari ty are discussed.

T h e fo rego ing pr inciples will be i l lustrated by such examples as (1) critical velocity f o r t u rbu len t mo t ion in pipes, wi th extension to

non -Newton i an mater ia l s ; (2 ) the viscosity e f fec t in Ventur i tubes ; (3 ) resis tance t o the m o v e m e n t of bodies t h rough a fluid, including

the mot ion of a roll ing ball in a t u b e of l iquid; (4 ) windage resis tance of ro ta t ing bodies ; (5 ) propel lers and st i rrers; and ( 6 ) fluid f i lm lub-ricat ion.

The Viscosity of Liquid Mixtures: Ideal and Non-Ideal Behavior R. H. Ewell, P u r d u e Univers i ty

Since it ha s been shown tha t f l o w can be successful ly t reated as

6.

a un imolecular rate process, f low in a m i x t u r e of l iquids can be con-sidered as ana logous to several un imolecular reactions, which yield the s ame product , p roceeding s imul taneous ly in the s ame vessel. Th i s concept leads directly to the ideal law i> - Z whe re N = m o l e f r ac t ion . Th i s relation is ana logous in f o r m and in " ra ison d ' e t r e " to the t h e r m o d y n a m i c ideal l a w s :

P - E N i P °

V - z NiVf

H - Z NjH°

where p = vapor pressure , V = mola r volume, H = mola r heat conten t . Whi le these re la t ions give the " idea l " behavior , they do not give

the " n o r m a l " behavior . T h e " n o r m a l " behavior is tha t of small pos-itive devia t ions f r o m the laws, since the van der W a a l s energy be tween t w o unl ike molecules , E a b , is equa l to Em Ebb, which is a lways less than the average of the energies be tween the like molecules , i. e.,

(E® +Ebb)/2. Since the normal behavior is an expans ion on mixing, the viscosity of a mix tu re will be g iven b y :

* - s % *S • '̂ 'T A 7

l ^ T h a s a v a l u e 1 0 t o 2 0 f o r m o s t l iquids. T h e surpr is ingly large value of this coeff ic ient is just the reason w h y the ideal law of mix tu re s f o r viscosity has no t been recognized in the past by exper imen ta l workers .

S t ruc tu re changes on mix ing lead to more p r o n o u n c e d devia t ions f r o m ideal. If hydrogen bonds are broken, e. g., in mix tu re s of benzene and ' a l coho l , large posit ive devia t ions occur. If hydrogen bonds are f o r m e d , e. g., in mix tu re s of ace tone and ch lo roform, large negat ive devia t ions occur. If hyd rogen bonds are both broken and fo rmed , both posi t ive and negat ive devia t ions occur in d i f fe ren t concen t ra t ion ranges, e. g., in mix tu re s of ch lo ro fo rm and alcohol.

A sys temat ic classification of the viscosity ( a n d other p roper t i es ) of liquid mix tu re s is developed on this basis, and practically comple te ag reemen t wi th expe r imen t is observed.

Viscosity and Constitution E. P. Irany, Shawin igan Chemicals , Ltd. C a n a d a

T h e inter-molecular forces are still neglected in ou r cur ren t con-cepts of liquid viscosity. T h e normal p a r a f f i n s usual ly provide the tes t ing g round for new empirical rules of cons t i tu t iona l ly addit ive vis-cosity, but a m o n g the m e m b e r s of this series, the inter-molecular forces are negligible, and ag reemen t is decept ively easy. T h e result is most ly

7.

an invalid genera l iza t ion inc luding subs tances of p ronounced polari ty, supp lemen ted by arb i t ra ry "associa t ion f ac to r s " .

According to graphical evidence, the general viscosity f u n c t i o n con ta ins at least t w o i ndependen t cons t i tu t ive pa ramete r s . In t ruly po lymer -homologous series o n e p a r a m e t e r is cons tan t , the o the r add-i t ive; in these cases, cons t i tu t ional analysis of viscosity is possible by graphical methods , us ing func t i ona l viscosity scales.

Some Relations Between Chemical Structure and Plasticizing Effect A. Kirkpatr ick, M o n s a n t o Chemica l Co., St . Louis, Mo.

T h e inter-relat ion be tween the chemical cons t i tu t ion and struc-ture of plast icizers and plastics is discussed. T h e resul ts obta ined wi th Su l fonamide , Ph tha la t e and P h o s p h a t e plasticizers in cellulose aceta te compos i t ions are used as examples and the au tho r speculates on the possibili ty of f o r m u l a t i n g genera l rules f r o m such data .

The Thermoelastic Properties and The Equation of State of Rubber F. E. Dar t and E. G u t h , Univers i ty of Notre D a m e

T h e high reversible elasticity and the a n o m a l o u s thermoelas t ic behavior of rubber 'are explained in t e rms of the molecular s t ruc tu re of rubber wi thou t m a k i n g any arbi t rary assumpt ions . Rubber consis ts of large chain molecules which can have a more or less curved fo rm , d u e to the possibility of f ree ro ta t ions a round single C - C bonds. Th i s curved f o r m is the most probable one according to the statistical inter-pre ta t ion of the second law of t h e r m o d y n a m i c s . If a stress is applied these curved molecules will be s t ra ightened, t h u s giving a t ransi t ion to a less probable state. W h e n the stress is released, the thermal agita-t ion causes a re t ract ion. Rubber elasticity is then ana logous to the el-asticity of a gas or l iquid.

C u r v e s giving the thermal s tate equa t ion for some pure g u m rubber samples will be s h o w n toge ther with cu rves showing the re-producibi l i ty of the results and the dependence of the stress-strain hysteres is loops upon the n u m b e r of ex tens ions and the t empera tu re . T h e thermal s tate equat ion and the so-called caloric s tate equa t ion to-gether de te rmine comple te ly the t h e r m o d y n a m i c s of stretched rubber .

Theoretical Consideration Concerning the Viscosity of Binary Silicate Glasses

R. H. Ewell, P u r d u e Univers i ty

Energy considera t ions dictate that the unit of f l ow in any silicate glass shall include only one silicon a tom. T h e w o r k of W a r r e n shows that in soda-silica glasses each silicon is su r rounded by f o u r bonds which m a y be Si-O-Si covalent bonds or Si-O ( ¡ ¿ p - S i electrostat ic

8.

bridges. T h e ene rgy required to break the f o r m e r bond is 100 ,000 cal. and the lat ter about 74 ,000 cal., including electrostatic, van der W a a l s and repulsive energies . Five possible un i t s of f l ow are the re fo re dis-t inguished according to w h e t h e r a given silicon has O , 1, 2, 3 or 4 of the 100 ,000 cal. bonds replaced by 74 ,000 cal. bonds . A s s u m i n g tha t the en t ropy of act ivat ion of f l ow is the s ame for all f ive un i t s of f low and that f l o w in a m i x t u r e is g iven b y t>«£-Ni ^ , a quan t i t a t ive ex-pression f o r the viscosity of a soda-silica glass as a f u n c t i o n of the com-posit ion is derived. T h e relation agrees well with exper imenta l da ta and appears to be based on an essential ly correct m e c h a n i s m . Th is view is ent irely at odds with the v iews of Pres ton and Seddon on com-pound fo rma t ion in glasses and their in terpre ta t ion of the i r regular w a v e s somet imes observed in the viscosi ty-composi t ion curves of b ina ry glasses It seems probable tha t these w a v e s are not real, but are due to poor da ta .

Recent Developments in the Study of Viscosity of Lubricating Oils at High Pressure.

R. B. D o w , Pennsy lvan ia S ta te College

P rev ious invest igat ions repor ted f r o m this labra tory have s h o w n tha t the pressure coeff ic ient of viscosity of lubr icat ing oils depends to a high degree u p o n the na tu re of the crude. M e a s u r e m e n t s were m a d e wi th the rolling-ball type of high pressure v iscometer . Recent s tudies have been m a d e wi th a Margule ' s concent r ic cyl inder visco-m e t e r adapted to high pressure measu remen t s . Th i s i n s t rumen t check-ed a rolling-ball v i scometer over the s ame pressure and t empe ra tu r e range , us ing the s ame sample of oil. An Extrac t and Ra f f i na t e were p roduced by an ace tone solvent ext rac t ion process f r o m a Pennsy l -vania oil; their pressure coeff ic ients of viscosity were similar to those of a coastal oil of low V. I. and a Pennsy lvan ia oil of high V. I., respect-ively, t h u s subs tan t ia t ing p rev ious m e a s u r e m e n t s of the au thor . Six P e n n s y l v a n i a oils, re f ined in var ious ways , and of var ious molecular weigh ts and boiling point r anges have been studied to obtain correla-t ion of chemical and physical proper t ies wi th pressure coeff ic ient of viscosity.

Pressure and Temperature Effects on Viscosity H e n r y Eyring, J o h n F. Kincaid and David Frisch, Pr ince ton Univers i ty

T h e general statistical theory of react ion rates as applied to vis-cosi ty will be g iven in out l ine. T h e f ree ene rgy of act ivat ion for vis-cous f l ow is related to an en t ropy and energy of act ivat ion by the same equa t ions as f o r any equi l ibr ium. This , f o r the theory of viscosity, is per fec t ly genera l and independen t of the m e c h a n i s m . T h e roll ing over

9.

each o ther of pairs of molecules lying in ad jo in ing layers seems to be the most probable mechan i sm. However , molecules can only roll pas t each o ther if there is a hole in the liquid about a third the size of the molecules in the p rope r place. If there is no external pressure such a hole involves an act ivat ion ene rgy of about one third the ene rgy of vapor iza t ion . At h igher pressures the work d o n e in f o r m i n g the hole against the external pressure m u s t be added. T h e rela t ionship be tween viscosity and d i f fus ion will also be discussed as well as the changes in these proper t ies which a c c o m p a n y f reez ing .

Viscosity of CCU-CS2 Mixtures of Liquids at High Pressure R. B. Dow, Pennsy lvan ia State College

T h e v iscos i ty- tempera ture character is t ics of CCI4-CS2 m ix tu re s have been studied over a pressure range of 10 ,000 K g / c m 2 . T h e con-cen t ra t ions were 15, 30, 50, 65, and 7 5 % by v o l u m e of CSg . Bridg-m a n ' s fal l ing weight v iscometer was used for the measu remen t s . T h e results obta ined and their s ignif icance to theories of viscosity is dis-cussed at length, par t icular ly f r o m the point of view of associat ion, molecu la r inter locking, and act ivat ion energy (Andrade ; Eyr ing and Ewel l ) . Scho t tky ' s theorem is applied to show tha t a character is t ic equa t ion of s tate is no t k n o w n tha t is applicable to the in ternal ene rgy changes of viscous f l ow at high pressure at cons tan t t empera tu re .

A Thermodynamic Theory of the Strength of Materials* M. Reiner, J e rusa l em, Palest ine, and K. Weisenberg ,

S o u t h a m p t o n , England

It is well k n o w n tha t in the ord inary tensile test of steel the s t reng th of the testpiece, as indicated by the tes t ing mach ine is con-siderably increased with increased speed of de fo rma t ion . A dynamica l theory of s t rength of materials , which takes account of the velocity of de fo rmat ion , ha s been worked out by Reiner and F reuden tha l (Congress for Applied Mechanics 1938, Cambr idge , Mass., U .S .A. ) . This ' is n o w f o u n d e d upon T h e r m o d y n a m i c s . " F a i l u r e " of a s t ruct-ural e lement , e i ther t h rough excessive (plast ic) de fo rma t ion or t h rough rup tu re , is accordingly governed by a m a x i m u m value of the intrinsic f ree energy, which can be "s tored u p " in the e lement It is s h o w n that this carries with it as a consequence that the fa i lure-stress of an elastic mater ial , which s h o w s d a m p i n g of its f ree oscilla-t ions increases with increasing velocity of strain. Th i s expla ins the p h e n o m e n o n m e n t i o n e d in the first sen tence above.

* This paper arrived too late for inclusion in the program, and will be read by title only.

10.

A REPORT ON RHEOLOGICAL DEFINITIONS AND NOMENCLATURE

Foreword In the fo l lowing repor t by the C o m m i t t e e on Def in i t ions and

Nomenc la tu re , an a t t emp t is m a d e to develop a complete , logical and self-consis tent sy s t em of classification of mater ia l s according to their rheological propert ies . It is in tended tha t t h e sys tem shall p rov ide a classification for all conceivable types of behavior of mater ia l s in de-f o r m a t i o n . T h e sys tem has been developed on the basis of cu r ren t usage to the ex ten t pe rmi t ted by logic and self-consis tency.

The classification and the a c c o m p a n y i n g def in i t ions h a v e been developed in t e rms of idealized mater ia ls t o which actual mater ia l s can be compared . In o ther words, ideal types of behavior and de fo rma-t ion are pos tu la ted which are suscept ible of exact def in i t ion and class-if icat ion. Actual mater ia ls can then be described in t e r m s of the ideal t ypes to which their behavior approx ima tes . It should be borne in mind tha t an actual mater ia l wi th rheological proper t ies coinciding exac t ly wi th those of a single idealized mater ia l is the except ion ra ther t han the rule. In app ly ing to actual mater ia l s the quan t i t a t ive def in i t ions f o r idealized mater ials , great caut ion m u s t be used.

It is recognized tha t the classif icat ion of a par t icular mater ia l m a y some t imes depend u p o n the m e t h o d of m e a s u r e m e n t . Th i s is par t icular ly t r u e as applied to the precision a t ta ined. T h e recogni t ion of a measu reab le "yield s t ress , " fo r example , m a y depend u p o n the pre-cision of t h e m e a s u r e m e n t and u p o n the dura t ion of the test . These uncer ta in t ies in the classification of mater ia l s result f r o m the fact tha t it is some t imes ei ther impossible or u n i m p o r t a n t to de te rmine f o r actual mater ia l s s o m e of the character is t ics which can be theoret ical ly dis-t inguished.

In this sys tem of classif icat ion and def ini t ions , only shear ing s t ra ins and stresses a re of interest , and the re la t ions involved are expressed wi th re fe rence to s imple shear . M a n y of the concep t s def ined here in t e r m s of s imple shear are closely related to those usual ly de-f ined by engineers in t e rms of m o r e complex t ypes of d e f o r m a t i o n , such as those aris ing in tens ion and compress ion tests. These defor -mat ions , while involv ing s imu l t aneous shears in three d imens ions and hence analyt ical ly complex , are o f t en easier to p roduce exper imenta l ly t han a simple shear . T h e y the re fo re se rve as a basis fo r m a n y use fu l and practical concepts a n d def in i t ions in the field of eng ineer ing . W h e r e an analysis of the f u n d a m e n t a l behavior of the mater ia l in de fo rma t ion is required, these eng inee r ing tes ts m a y be reduced to a combina t ion of shears, and described in t e r m s of the concepts used in this repor t .

11.

A genera l relation be tween strain and stress applies to any poin t wi th in a mater ia l , and except in ex t r ao rd ina ry c i rcumstances , these values will vary at d i f fe ren t points . T h e quan t i t i e s involved in these re la t ions apply ing to individual poin ts wi th in the mater ia l canno t be observed directly. Obse rvab l e quant i t ies such as e f f lux- ra te , pressure , etc., can be obta ined by in tegra t ing the basic po in t re la t ions and can then be compared wi th the values obta ined exper imenta l ly . It is, h o w -ever, a lways possible, at least fo rmal ly , to devise expe r imen t s and m e t h o d s of analysis by which the f u n d a m e n t a l re la t ionship can be comple te ly de te rmined f r o m exper imenta l data .

A l though all mater ia ls exhibit the inertia e f fec t s associated wi th acceleration of the m a s s e lements wi th in the mater ial , these e f fec t s are ignored as be ing i rrelevant in the classification and def in i t ions g iven below. It should be noted tha t tu rbu lence and related h y d r o d y n -amical proper t ies belong in this ca tegory .

Descriptive Definitions Cons i s t ency is the resistance to f l ow of a mater ia l (See Q u a n t i t -

at ive D e f i n i t i o n s ) .

Plas t ic i ty is t ha t p rope r ty of a body by vi r tue of which it re ta ins a f rac t ion of its d e f o r m a t i o n a f t e r reduct ion of the d e f o r m i n g stress to zero.

Elast ici ty is t ha t p roper ty of a body by vi r tue of which it recovers its original size and shape a f t e r de fo rma t ion .

T h i x o t r o p y is tha t p roper ty of a body by vi r tue of which its con-s is tency is reduced by prev ious de fo rma t ion .

S t r a in h a r d e n i n g is tha t p roper ty of a body by vi r tue of which the s t ress required f o r p e r m a n e n t de fo rma t ion increases with the ex ten t of p rev ious p e r m a n e n t de fo rma t ion .

Hys teres is is tha t p roper ty of a body by vi r tue of which the rela-tion be tween stress and strain for decreas ing stress d i f f e r s f r o m tha t f o r increasing stress. Materials exhibi t ing hysteres is are k n o w n as hysteretics.

A f lu id is a subs tance which undergoes c o n t i n u o u s d e f o r m a t i o n w h e n subjected to shear stress.

A solid is a subs tance which unde rgoes p e r m a n e n t d e f o r m a t i o n or r u p t u r e only w h e n subjec ted to shear stress in excess of a certain m i n i m u m value.

Quantitative Definitions A s imple shea r is a de fo rma t ion in which the mater ia l at any

point has moved parallel to a f ixed line in a re fe rence plane by an

12.

a m o u n t which is p ropor t iona l to the d is tance of the poin t f r o m the plane. Such a de fo rma t ion is s h o w n in F igure 1, the fu l l l ines showing the initial shape and the dot ted lines the f inal shape . O O is the f ixed line in the re fe rence plane, P is the original posi t ion of a point in the body, and P ' its posi t ion a f t e r de fo rma t ion . T h e shear strain, e , is g iven by the rat io of the d isp lacement ds to the dis tance dx of the point P f r o m O O , or e = d s / d x .

T h e ang le of shear is the angle whose t a n g e n t is the shear s t ra in . In F igure 1 the angle a is the angle of shear (a = t a n " 1 d s / d x ) .

T h e r a t e of »hear is the t ime ra te of c h a n g e of shear s t ra in . In Figure 1 the ra te of shear is g iven b y :

dv a . d s dx d t v d x '

A c o m p l e x shear is the resul tant of t w o or m o r e s imple shears . Fo r simplicity, the def in i t ions g iven in this repor t are s tated in t e rms of s imple shear, it being unders tood tha t the s ame def in i t ions apply in the case of complex shears resu l t ing f r o m simple shears of the s ame type .

T h e cons is tency of a mater ia l is the rat io of the shear s t ress to the ra te of shear .

T h e viscosity of a s imple liquid is the cons tan t ratio of shear stress to the ra te of shear .

N o t e : T h e t e rm "v i scos i ty" is applied only to s imple liquids. How-ever, the adjec t ive " v i s c o u s " does not necessari ly imply a l inear relation be tween shear s t ress and rate of shear and is used in the m o r e general sense in the t e r m "plas t ico-viscous" , def ined below.

T h e poise is the unit of viscosity in the C .G.S . sys tem.

T h e f lu id i ty of a s imple liquid is the reciprocal of the viscosity.

T h e rhe is the unit of f lu idi ty in the C .G.S . sys tem.

T h e m o b i l i t y j i is the quan t i ty def ined by the e q u a t i o n :

dv

charac ter iz ing the de fo rma t ion of a body for which the rate of shear •Jx i s a l i n e a r f u n c t i o n of the shear stress F for s tresses grea te r t han the yield stress F Q , and is zero for stresses less t han J^ .

T h e yield s t ress of a solid is the shear stress which m u s t be equal-led or exceeded to p roduce p e r m a n e n t de fo rma t ion .

T h e elastic l imit in shear of a solid is the m a x i m u m de fo rma t ion

13.

tha t is elastic and the m i n i m u m d e f o r m a t i o n tha t resul ts in r u p t u r e or in p e r m a n e n t d e f o r m a t i o n .

T h e shear s t r e n g t h of a solid is the m i n i m u m value of shear s t ress at which macroscopic r u p t u r e occurs.

T h e shear m o d u l u s of elasticity ( m o d u l u s of r igidi ty) of an elastic solid is the cons tan t ratio of shear s t ress to shear s train f o r va lues of the shear s t ra in be low the elastic limit.

Classification

T h e classif icat ion of idealized types of mater ia ls is in t e rms of their behav ior unde r load, or the relat ion be tween strain and stress. T h e s t ress at any point wi th in a mater ia l is a f u n c t i o n of the s t ra in and its t ime der ivat ive, or r a t e of s t ra in . In all mater ia l s the second t ime der ivat ive of s train de te rmines the inertia e f fec t . As noted above, this e f fec t is ignored in these def in i t ions .

T h e stress m a y depend to some ex ten t on the prior s train or de fo rma t ion his tory of the mater ia l . Such dependence upon the prior s t ra in is regarded f o r conven ience as a secondary characterist ic , m a t -erials be ing classified pr imari ly by the actual relation be tween stress and i n s t an t aneous strain or ra te of s t ra in wi thou t regard to d i f fe rences in this re la t ionship tha t would result f r o m a d i f fe ren t s train his tory .

Classes of Fluids (a ) A gas is a f lu id dis t inguished f r o m a liquid by its behavior

unde r hydros ta t ic pressure changes . Th i s dist inct ion is i r re levant to this classif ication, as it does no t involve shear stresses. Under shear stress the behavior of a gas is identical wi th tha t of a s imple liquid.

(b ) A s imple l iquid ( N e w t o n i a n l iquid) is one for which the ra te of shear is p ropor t iona l to the shear stress. Symbol ica l ly :

„ I p (See S u m m a r y ) dx i\

(c) A complex l iquid (Non-Newton ian l iquid) is o n e f o r which the ra te of shear is a f u n c t i o n of shear stress only, this f u n c t i o n being o the r t han tha t of direct propor t ional i ty . Symbol ica l ly :

= f ( f ) > 0 (See S u m m a r y )

Classes of Solids ( a ) An elastic solid is one for which the shear s train is a single

va lued m o n o t o n i c f u n c t i o n of the shear stress for all va lues of the

14.

la t ter below the shear s t rength . Symbol ica l ly :

e - f ( ? ) > O, > 0 , 0 < 7 < F a (See S u m m a r y )

(b ) A H o o k i a n solid is an elastic solid for which the shear s train is directly propor t iona l to the shear stress for all va lues of the la t ter be low the shear s t rength . Symbol ica l ly :

p e 0 < P < p Q (See S u m m a r y )

Reduct ion of the shear ing stress to zero resul ts in the immedia te and comple te d i sappearance of the s t ra in .

(c) A plast ic solid is one which obeys the law of an elastic solid f o r shear stress below the yield stress, and for shear stress in excess of this value is p e r m a n e n t l y d e f o r m e d at a rate control led only by the inertia react ion. Symbol ica l ly :

E = f ( P ) > 0 , o , 0 < P < p 0

d v (See S u m m a r y ) e > o , s > o . p 0 < F < P q

Reduct ion of the shear stress to zero results in an immedia te recovery of the elastic por t ion of the strain. T h e strain in excess of tha t exper ienced up to the yield point r emains as p e r m a n e n t de fo rma t ion .

(d ) A plast ico-viscous solid is one for which the de fo rma t ion for shear stress below the yield stress is tha t of an elastic solid, and which for shear s t ress above that value de fo rms con t inuous ly at a ra te of shear which is a f u n c t i o n of the shear stress. Symbol ica l ly :

e - f ( P ) > 0 , ^ f > 0 , 0 < P < P q

g - f ( F ) > 0 , P 0 < P < P c

(See S u m m a r y )

Reduct ion of the shear stress to a value below the yield stress results in the immedia te reduct ion of the rate of shear to zero. The

strain in excess of tha t exper ienced up to the yield point r emains as p e r m a n e n t de fo rma t ion .

(e ) A c o m p l e x solid is one for which the shear stress required for de fo rma t ion is a func t ion of both the shear strain and rate of s t ra in . Symbol ica l ly :

6 - f (F, f t , Prior Strain x

The classification g iven above is wi thou t regard to prior strain. W h e n the t e rms def ined above are used wi thou t qual i f icat ion it is implied tha t the stress-strain relation is independen t of the strain previous ly exper ienced. Materials fo r which the stress-strain relation

15.

is dependent on prior strain should be described as Thixot ropic or Strain Harden ing in the senses in which these te rms are defined above.

Rheological Diagram

It is recommended that wherever possible published data on complex liquids should include not only the observed quanti t ies such as pressure, t ime of e f f lux , etc., but in addition the calculated basic quanti t ies. The preferred curve should show consistency, fluidity, or rate of shear plotted against shear stress, rather, than e f f lux rate against pressure, or rate of rotation against torque. Rheological C u r v e or Rheological Diagram are suggested as short convenient te rms for curves of these preferred types.

SU1HARY" OF RHEOLOGICAL NOMENCLATURE

P ds P* rv I - - ; / / " / / ; /

B: Linear displacement parallel to direction of deforma-tion.

x: Linear coordinate in the plane of the deformation and normal to direction to deformation,

v-ds/dt: linear velocity, dv/dx: Rate of shear.

F: Shearing stress. £»ds/dx: shear strain.

Po: Yield stress. Shearing stress at rupture (shear strength).

H: Coefficient of viscosity. G: Shear modulus of elasticity (modulus of rigidity) p: Coefficient of mobility.

p/~*. Consistency.

16.

7 / /

/ a

/ 0

Figure 1 Simple Shear

Fluids

(a) Gas

dr „ I p dx II

(b) Simple Liquid

i l a - F di I)

(c) Complex Liquid

g - f ( » ) > 0

2. Solids

(a) Elastic Solid

e - f ( F ) > 0 , 0 < F < F a

(b) Hookian Solid

e - f , 0 < F < F a

(c) Plastic Solid

£ » f (F) > 0 , 0 < F < F q

£ > 0, g > 0, F0< F<F a

(d) Plastico-Viscous Solid

e- f (F) > 0 , 0 < F < F 0

g f(F) > 0, F 0 < F < F a

(e) Complex Solid

F m , g ,

- 17 -

THE SOCIETY OF RHEOLOGY

Pres. Melvin M o o n e y Edi tor W h e e l e r P . D a v e y 1st Vice-Pres. A. S. H u n t e r Sec.-Treas . R. L. Peek, J r . 2nd Vice-Pres. E. C . B i n g h a m

T h e Socie ty of Rheology was f o u n d e d in 1929 to f u r t h e r the s tudy of the d e f o r m a t i o n and flo-w of ma t t e r . Th i s pu rpose has been in te rpre ted in the broadest sense, as cover ing types of d e f o r m a t i o n r a n g i n g f r o m the viscous f low of f luids, t h rough the plastic f low of sof t subs tances , to the elastic d e f o r m a t i o n of solids. Rheology m a y be regarded as the science whose industr ial appl ica t ion cons t i tu t e s the field of ma te r i a l s tes t ing.

Pape r s deal ing with Rheology are presented to the Society at its a n n u a l mee t ing , and are submi t t ed for publ ica t ion in the J o u r n a l of Applied Physics, a subscr ipt ion to which is included in the dues of regular m e m b e r s . Regula r m e m b e r s also receive the Rheology Leaf-let. which is publ ished quar te r ly . T h e Leafle t serves as a m e d i u m for n e w s of the Society and of o ther o rgan iza t ions and special mee t ings concerned with Rheology . It also provides abs t rac ts and reviews of rheological l i tera ture .

Associate m e m b e r s receive the Leafle t only . Sus t a in ing m e m -bers pay dues of § 2 5 or more , which serve to subs tan t ia l ly suppo r t the Soc ie ty ' s activities. As a part ial re tu rn f o r these dues they receive subscr ip t ions to the J o u r n a l of Applied Physics , the Review of Scientif ic I n s t r u m e n t s and the Rheo logy Leaflet .

Membersh ip is f o r the ca lendar yea r and n e w m e m b e r s receive the issues of the jou rna l publ ished prior to their appl icat ions . Af te r S e p t e m b e r 1, appl icat ion m a y be made , if desired, f o r m e m b e r s h i p to s tar t J a n u a r y 1 of the yea r fo l lowing .

T h e Society of Rheology is one of the m e m b e r societies of the Amer ican Ins t i tu te of Physics , and its m e m b e r s are enti t led to sub-scribe to the fo l lowing addit ional journa l s publ ished by the Ins t i tu te , at the ra tes s h o w n :

Domestic Foreign Physical Rev iew S I 5 . 0 0 $ 1 6 . 5 0 Reviews of Modern Phys ics 3 .00 3 .40 J o u r n a l of the Opt ica l Society of America 6 . 0 0 6 .60 Review of Scient i f ic I n s t r u m e n t s 1 .50 2 .00 J o u r n a l of the Acoustical Socie ty of Amer ica 6 .00 6.60 J o u r n a l of Chemical Physics 10 .00 11.00 Amer ican Phys ics Teacher 5 .00 5 .50

APPLICATION

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1 he r eby app ly f o r m e m b e r s h i p in the Socie ty of Rheo logy f o r the yea r as f o l l o w s :

[ ] Sus t a in ing m e m b e r s h i p ( inc lud ing subscr ip t ions t o bo th J o u r n a l of Appl ied Physic« and R . S . I. $ 2 5 . 0 0 or m o r e

[ ] Regula r m e m b e r s h i p ( inc lud ing subscr ip t ion t o J o u r n a l of Appl ied Phys ic«) $ 6 . 0 0 ( fo re ign , $ 6 . 5 0 )

[ ] Associate m e m b e r s h i p $ 2 . 0 0 ( fore ign , $ 2 . 5 0 )

All m e m b e r s receive a subscr ip t ion t o t h e Rheo logy Leaf le t .

P lease also en t e r m y subscr ip t ion f o r t h e f o l l o w i n g addi t ional periodicals publ i shed by t h e Amer i can Ins t i tu te of Phys i c s :

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